In the first column of the table, the distance ac or the actual cutting distance is given; the second, third and fourth columns give corresponding distances bc, when the clearance angles are 10, 15 and 20 degrees, respectively. To illustrate the use of the table, suppose a tool is required for turning the piece shown in Fig. 1, having diameters of 0.75, 1.25 and 1.75 inch, respectively. Reducing these diameters to their respective radii, we have 0.375, 0.625 and 0.875. The difference between the largest and smallest radii is 0.5, which would equal the actual cutting edge of the tool or dimension ac. Assume = that the tool is to be set at an angle of 15 degrees. The distance ac, or 0.5, is located in the column headed "Actual Cutting Distance," and then the corresponding value for bc in the 15-degree column. As will be seen, bc 0.48296. In the same way, the depth of the second step on the tool is determined. As the difference in radii equals 0.25, length bc for a 15-degree angle equals 0.19318+ 0.04829 = 0.24147. If the forming tool is made so that the steps measure 0.4830 and 0.2415, respectively, along the line bc, the diameters turned will correspond to those given, provided the cutting face of the tool is central with the work, and the front face held so that the clearance angle is 15 degrees. Fig. 1 Sometimes it is necessary to turn an angular surface. The table "Angles for Straight Forming Tools" gives the required angle for the tool face for turning Angles for Straight Forming Tools the work to a given angle. These angles are not alike, because of the clearance angle of the tool. They are measured from the center-line of the piece or, what-is equivalent, from the formed face of the tool. For example, what angle a (see illustration in table) should a forming tool have to turn a surface to an angle of 40 degrees (see Fig. 1), assuming that the clearance angle of the forming tool is 15 degrees? Find angle a in the first column of the table and then the corrected angle in the column headed "ẞ = 15 degrees." The corrected angle in this case is 39 degrees 1 minute. Circular Forming Tools. To provide sufficient periphery clearance on circular forming tools, the cutting face is off-set with relation to the center of the tool a distance C as shown in Fig. 2. Whenever a circular tool has two or more diameters, 1 Fig. 2 the difference in the radii of the steps on the tool will, therefore, not correspond exactly to the difference in the steps on the work. The form produced with the tool also changes, although the change is very slight, unless the amount of off-set C is considerable. Assume that a circular tool is required to produce the piece A having two diameters as shown. If the difference Di be tween the large and small radii of the tool were made equal to dimension D required on the work, D would be a certain amount over-size, depending upon the off-set C of the cutting edge. The following formulas can be used to determine the radii of circular forming tools for turning parts to different diameters: then: D= difference in radii of steps on work; C amount cutting edge is off-set from center of tool; r = required radius in inches; If the small radius r is given and the large radius R is required, then: R = √(√r2 – C2 + D)2 + C2. (1) (2) To illustrate, if D (Fig. 2) is to be % inch, the large radius R is 1% inch, and C is 32 inch, what radius r would be required to compensate for the off-set C of the cutting edge? Inserting these values in Formula (1): The value of r is thus found to be 1.0014 inch; hence the diameter = 2 X 1.0014 = 2.0028 inches instead of 2 inches, as would have been the case if the cutting edge had been exactly on the center-line. This formula, when applied to the circular tools used on the Brown & Sharpe automatic screw machines, can be simplified by inserting the values R and C, these being constant for each size of machine. The length of the blade equals radius of stock R +x+r+32 inch (for notation see illustration above); r = 0 inch for %- to 4-inch stock, and 32 inch for 4- to 1-inch stock. The formula will then have the following form: No. o Brown & Sharpe automatic screw machine, ☛ = √ (1.114 — D)2 + 0.0244. 1= No. 2 Brown & Sharpe automatic screw machine, r = √ (1.479 — D)2 + 0.0625. The table "Constants for Determining Diameters of Circular Forming Tools" has been compiled to facilitate proportioning tools of this type. It gives constants for computing the various diameters of forming tools, when the cutting face of the tool is either 8, 10, 4 or 16 inch below the horizontal center-line. As there is no standard distance for the location of the cutting face, the table has been prepared to correspond with distances commonly used. As an example, suppose the tool is required for a part having three diameters of 1.75, 0.75 and 1.25 inch, respectively, as shown in Fig. 1, and that the largest diameter of the tool is 3 inches and its cutting face is 14 inch below the horizontal center-line. The first step would be to determine approximately the respective diameters of the forming tool and then correct these diameters by the use of the table. To produce the three diameters shown in Fig. 1, with a 3-inch forming tool, the tool diameters would be approximately 2, 3 and 2.5 inches, respectively. The first dimension (2 inches) is 1 inch less in diameter than that of the tool, and the necessary correction should be given in the column "Correction for Difference in Diameter"; but as the table is only extended to half-inch differences, it will be necessary to obtain this particular correction in two steps. On the line for 3-inch diameter and under corrections for 1⁄2 inch, we find 0.0085; then in line with 22 and under the same heading, we find 0.0129; hence the total correction would be 0.0085 + 0.0129 = 0.0214 inch. This correction is added to the approximate diameter, making the exact diameter of the first step 2 +0.0214 2.0214 inches. The next step would be computed in the same way, by noting on the 3-inch line the correction for 1⁄2 inch and adding it to the approximate diameter of the second step, giving an exact diameter of 2.5+ 0.00852.5085 inches. Therefore, to produce the part shown in Fig. 1, the tool should have three steps of 3, 2.0214 and 2.5085 inches, respectively, provided the cutting face is 4 inch below the center. All diameters are computed in this way, from the largest diameter of the tool. The tables "Corrected Diameters of Circular Forming Tools" are especially applicable to tools used on Brown & Sharpe automatic screw machines. Directions for using these tables are given at the end of Table 4. Most circular forming tools are made without top rake, that is, the cutting edge is in a horizontal plane, as illustrated in Fig. 2. Tools made in this way are especially adapted for cutting brass but may not work entirely satisfactorily on tougher and harder metals. The amount of top rake for circular tools varies from o to approximately 18 degrees. For general conditions, the following angles for top rake are recommended: Rod brass, o degrees; drill rod and tool steel, 8 to 10 degrees; gun-screw iron, 12 degrees; machine steel, 15 degrees; Norway iron, 18 degrees; aluminum, 25 to 30 degrees; German tubing, 25 to 35 degrees. When a circular forming tool is given top rake, corrections for the diameters of different steps must be made, the variation in diameter depending upon the angle of rake. The rather lengthy mathematical calculations involved are given in full in MACHINERY'S Reference Book, No. 101, "Automatic Screw Machine Practice,' page 20. |